A Novel Reconfiguration Scheme in Quantum-Dot Cellular Automata for Energy Efficient Nanocomputing

Quantum-Dot Cellular Automata (QCA) is currently being investigated as an alternative to CMOS technology. There has been extensive study on a wide range of circuits from simple logical circuits such as adders to complex circuits such as 4-bit processors. At the same time, little if any work has been done in considering the possibility of reconfiguration to reduce power in QCA devices. This work presents one of the first such efforts when considering reconfigurable QCA architectures which are expected to be both robust and power efficient. We present a new reconfiguration scheme which is highly robust and is expected to dissipate less power with respect to conventional designs. An adder design based on the reconfiguration scheme will be presented in this thesis, with a detailed power analysis and comparison with existing designs. In order to overcome the problems of routing which comes with reconfigurability, a new wire crossing mechanism is also presented as part of this thesis

New Symmetric and Planar Designs of Reversible Full-Adders/Subtractors in Quantum-Dot Cellular Automata

Quantum-dot Cellular Automata (QCA) is one of the emerging nanotechnologies, promising alternative to CMOS technology due to faster speed, smaller size, lower power consumption, higher scale integration and higher switching frequency. Also, power dissipation is the main limitation of all the nano electronics design techniques including the QCA. Researchers have proposed the various mechanisms to limit this problem. Among them, reversible computing is considered as the reliable solution to lower the power dissipation. On the other hand, adders are fundamental circuits for most digital systems. In this paper, Innovation is divided to three sections. In the first section, a method for converting irreversible functions to a reversible one is presented. This method has advantages such as: converting of irreversible functions to reversible one directly and as optimal. So, in this method, sub-optimal methods of using of conventional reversible blocks such as Toffoli and Fredkin are not used, having of minimum number of garbage outputs and so on. Then, Using the method, two new symmetric and planar designs of reversible full-adders are presented. In the second section, a new symmetric, planar and fault tolerant five-input majority gate is proposed. Based on the designed gate, a reversible full-adder are presented. Also, for this gate, a fault-tolerant analysis is proposed. And in the third section, three new 8-bit reversible full-adder/subtractors are designed based on full-adders/subtractors proposed in the second section. The results are indicative of the outperformance of the proposed designs in comparison to the best available ones in terms of area, complexity, delay, reversible/irreversible layout, and also in logic level in terms of garbage outputs, control inputs, number of majority and NOT gates

New Symmetric and Planar Designs of Reversible Full-Adders/Subtractors in Quantum-Dot Cellular Automata

Quantum-dot Cellular Automata (QCA) is one of the emerging nanotechnologies, promising alternative to CMOS technology due to faster speed, smaller size, lower power consumption, higher scale integration and higher switching frequency. Also, power dissipation is the main limitation of all the nano electronics design techniques including the QCA. Researchers have proposed the various mechanisms to limit this problem. Among them, reversible computing is considered as the reliable solution to lower the power dissipation. On the other hand, adders are fundamental circuits for most digital systems. In this paper, Innovation is divided to three sections. In the first section, a method for converting irreversible functions to a reversible one is presented. This method has advantages such as: converting of irreversible functions to reversible one directly and as optimal. So, in this method, sub-optimal methods of using of conventional reversible blocks such as Toffoli and Fredkin are not used, having of minimum number of garbage outputs and so on. Then, Using the method, two new symmetric and planar designs of reversible full-adders are presented. In the second section, a new symmetric, planar and fault tolerant five-input majority gate is proposed. Based on the designed gate, a reversible full-adder are presented. Also, for this gate, a fault-tolerant analysis is proposed. And in the third section, three new 8-bit reversible full-adder/subtractors are designed based on full-adders/subtractors proposed in the second section. The results are indicative of the outperformance of the proposed designs in comparison to the best available ones in terms of area, complexity, delay, reversible/irreversible layout, and also in logic level in terms of garbage outputs, control inputs, number of majority and NOT gates

Architectural Solutions for NanoMagnet Logic

The successful era of CMOS technology is coming to an end. The limit on minimum fabrication dimensions of transistors and the increasing leakage power hinder the technological scaling that has characterized the last decades. In several different ways, this problem has been addressed changing the architectures implemented in CMOS, adopting parallel processors and thus increasing the throughput at the same operating frequency. However, architectural alternatives cannot be the definitive answer to a continuous increase in performance dictated by Moore’s law. This problem must be addressed from a technological point of view. Several alternative technologies that could substitute CMOS in next years are currently under study. Among them, magnetic technologies such as NanoMagnet Logic (NML) are interesting because they do not dissipate any leakage power. More- over, magnets have memory capability, so it is possible to merge logic and memory in the same device. However, magnetic circuits, and NML in this specific research, have also some important drawbacks that need to be addressed: first, the circuit clock frequency is limited to 100 MHz, to avoid errors in data propagation; second, there is a connection between circuit layout and timing, and in particular, longer wires will have longer latency. These drawbacks are intrinsic to the technology and for this reason they cannot be avoided. The only chance is to limit their impact from an architectural point of view. The first step followed in the research path of this thesis is indeed the choice and optimization of architectures able to deal with the problems of NML. Systolic Ar- rays are identified as an ideal solution for this technology, because they are regular structures with local interconnections that limit the long latency of wires; more- over they are composed of several Processing Elements that work in parallel, thus exploit parallelization to increase throughput (limiting the impact of the low clock frequency). Through the analysis of Systolic Arrays for NML, several possible im- provements have been identified and addressed: 1) it has been defined a rigorous way to increase throughput with interleaving, providing equations that allow to esti- mate the number of operations to be interleaved and the rules to provide inputs; 2) a latency insensitive circuit has been designed, that exploits a data communication protocol between processing elements to avoid data synchronization problems. This feature has been exploited to design a latency insensitive Systolic Array that is able to execute the Floyd-Steinberg dithering algorithm. All the improvements presented in this framework apply to Systolic Arrays implemented in any technology. So, they can also be exploited to increase performance of today’s CMOS parallel circuits. This research path is presented in Chapter 3. While Systolic Arrays are an interesting solution for NML, their usage could be quite limited because they are normally application-specific. The second re- search path addresses this problem. A Reconfigurable Systolic Array is presented, that can be programmed to execute several algorithms. This architecture has been tested implementing many algorithms, including FIR and IIR filters, Discrete Cosine Transform and Matrix Multiplication. This research path is presented in Chapter 4. In common Von Neumann architectures, the logic part of the circuit and the memory one are separated. Today bus communication between logic and memory represents the bottleneck of the system. This problem is addressed presenting Logic- In-Memory (LIM), an architecture where memory elements are merged in logic ones. This research path aims at defining a real LIM architectures. This has been done in two steps. The first step is represented by an architecture composed of three layers: memory, routing and logic. In the second step instead the routing plane is no more present, and its features are inherited by the memory plane. In this solution, a pyramidal memory model is used, where memories near logic elements contain the most probably used data, and other memory layers contain the remaining data and instruction set. This circuit has been tested with odd-even sort algorithms and it has been benchmarked against GPUs and ASIC. This research path is presented in Chapter 5. MagnetoElastic NML (ME-NML) is a technological improvement of the NML principle, proposed by researchers of Politecnico di Torino, where the clock system is based on the induced stretch of a piezoelectric substrate when a voltage is ap- plied to its boundaries. The main advantage of this solution is that it consumes much less power than the classic clock implementation. This technology has not yet been investigated from an architectural point of view and considering complex circuits. In this research field, a standard methodology for the design of ME-NML circuits has been proposed. It is based on a Standard Cell Library and an enhanced VHDL model. The effectiveness of this methodology has been proved designing a Galois Field Multiplier. Moreover the serial-parallel trade-off in ME-NML has been investigated, designing three different solutions for the Multiply and Accumulate structure. This research path is presented in Chapter 6. While ME-NML is an extremely interesting technology, it needs to be combined with other faster technologies to have a real competitive system. Signal interfaces between NML and other technologies (mainly CMOS) have been rarely presented in literature. A mixed-technology multiplexer is designed and presented as the basis for a CMOS to NML interface. The reverse interface (from ME-NML to CMOS) is instead based on a sensing circuit for the Faraday effect: a change in the polarization of a magnet induces an electric field that can be used to generate an input signal for a CMOS circuit. This research path is presented in Chapter 7. The research work presented in this thesis represents a fundamental milestone in the path towards nanotechnologies. The most important achievement is the de- sign and simulation of complex circuits with NML, benchmarking this technology with real application examples. The characterization of a technology considering complex functions is a major step to be performed and that has not yet been ad- dressed in literature for NML. Indeed, only in this way it is possible to intercept in advance any weakness of NanoMagnet Logic that cannot be discovered consid- ering only small circuits. Moreover, the architectural improvements introduced in this thesis, although technology-driven, can be actually applied to any technology. We have demonstrated the advantages that can derive applying them to CMOS cir- cuits. This thesis represents therefore a major step in two directions: the first is the enhancement of NML technology; the second is a general improvement of parallel architectures and the development of the new Logic-In-Memory paradigm

Emerging Technologies - NanoMagnets Logic (NML)

In the last decades CMOS technology has ruled the electronic scenario thanks to the constant scaling of transistor sizes. With the reduction of transistor sizes circuit area decreases, clock frequency increases and power consumption decreases accordingly. However CMOS scaling is now approaching its physical limits and many believe that CMOS technology will not be able to reach the end of the Roadmap. This is mainly due to increasing difficulties in the fabrication process, that is becoming very expensive, and to the unavoidable impact of leakage losses, particularly thanks to gate tunnel current. In this scenario many alternative technologies are studied to overcome the limitations of CMOS transistors. Among these possibilities, magnetic based technologies, like NanoMagnet Logic (NML) are among the most interesting. The reason of this interest lies in their magnetic nature, that opens up entire new possibilities in the design of logic circuits, like the possibility to mix logic and memory in the same device. Moreover they have no standby power consumption and potentially a much lower power consumption of CMOS transistors. In literature NML logic is well studied and theoretical and experimental proofs of concept were already found. However two important points are not enough considered in the analysis approach followed by most of the work in literature. First of all, no complex circuits are analyzed. NML logic is very different from CMOS technologies, so to completely understand the potential of this technology it is mandatory to investigate complex architectures. Secondly, most of the solutions proposed do not take into account the constraints derived from fabrication process, making them unrealistic and difficult to be fabricated experimentally. This thesis focuses therefore on NML logic keeping into account these two important limitations in the research approach followed in literature. The aim is to obtain a complete and accurate overview of NML logic, finding realistic circuital solutions and trying to improve at the same time their performance. After a brief and complete introduction (Chapter 1), the thesis is divided in two parts, which cover the two fundamental points followed in this three years of research: A circuits architecture analysis and a technological analysis. In the architecture analysis first an innovative VHDL model is described in Chapter 2. This model is extensively used in the analysis because it allows fast simulation of complex circuits, with, at the same time, the possibility to estimate circuit per- formance, like area and power consumption. In Chapter 3 the problem of signals synchronization in complex NML circuits is analyzed and solved, using as benchmark a simple but complete NML microprocessor. Different solutions based on asynchronous logic are studied and a new asynchronous solution, specifically designed to exploit the potential of NML logic, is developed. In Chapter 4 the layout of NML circuits is studied on a more physical level, considering the limitations of fabrication processes. The layout of NML circuits is therefore changed accordingly to these constraints. Secondly CMOS circuits architectures are compared to more simple architectures, evaluating therefore which one is more suited for NML logic. Finally the problem of interconnections in NML technology is analyzed and solutions to improve it are found. In Chapter 5 the problem of feedback signals in heavy pipelined technologies, like NML, is studied. Solutions to improve performances and synchronize signals are developed. Systolic arrays are then analyzed as possible candidate to exploit NML potential. Finally in Chapter 6 ToPoliNano, a simulator dedicated to NML and other emerging technologies, that we are developing, is described. This simulator allows to follow the same top-down approach followed for CMOS technology. The layout generator and the simulation engine are detailed described. In the first chapter of the technological analysis (Chapter 7), the performance of NML logic is explored throughout low level simulations. The aim is to understand if these circuits can be fabricated with optical lithography, allowing therefore the commercial development of NML logic. Basic logic gates and the clock system are there analyzed from a low level perspective. In Chapter 8 an innovative electric clock system for NML technology is shown and the first experimental results are reported. This clock system allows to achieve true low power for NML technology, obtaining a reduction of power consumption of 20 times considering the best CMOS transistors available. This power consumption takes into account all the losses, also the clock system losses. Moreover the solution presented can be fabricated with current technological processes. The research work behind this thesis represents an important breakthrough in NML logic. The solutions here presented allow the design and fabrication of complex NML circuits, considering the particular characteristics of this technology and considerably improving the performance. Moreover the technological solutions here presented allow the design and fabrication of circuits with available fabrication process with a considerable advantage over CMOS in terms of power consumption. This thesis represents therefore a considerable step froward in the study and development of NML technolog

Fault and Defect Tolerant Computer Architectures: Reliable Computing With Unreliable Devices

This research addresses design of a reliable computer from unreliable device technologies. A system architecture is developed for a fault and defect tolerant (FDT) computer. Trade-offs between different techniques are studied and yield and hardware cost models are developed. Fault and defect tolerant designs are created for the processor and the cache memory. Simulation results for the content-addressable memory (CAM)-based cache show 90% yield with device failure probabilities of 3 x 10(-6), three orders of magnitude better than non fault tolerant caches of the same size. The entire processor achieves 70% yield with device failure probabilities exceeding 10(-6). The required hardware redundancy is approximately 15 times that of a non-fault tolerant design. While larger than current FT designs, this architecture allows the use of devices much more likely to fail than silicon CMOS. As part of model development, an improved model is derived for NAND Multiplexing. The model is the first accurate model for small and medium amounts of redundancy. Previous models are extended to account for dependence between the inputs and produce more accurate results

Fault tolerance issues in nanoelectronics

The astonishing success story of microelectronics cannot go on indefinitely. In fact, once devices reach the few-atom scale (nanoelectronics), transient quantum effects are expected to impair their behaviour. Fault tolerant techniques will then be required. The aim of this thesis is to investigate the problem of transient errors in nanoelectronic devices. Transient error rates for a selection of nanoelectronic gates, based upon quantum cellular automata and single electron devices, in which the electrostatic interaction between electrons is used to create Boolean circuits, are estimated. On the bases of such results, various fault tolerant solutions are proposed, for both logic and memory nanochips. As for logic chips, traditional techniques are found to be unsuitable. A new technique, in which the voting approach of triple modular redundancy (TMR) is extended by cascading TMR units composed of nanogate clusters, is proposed and generalised to other voting approaches. For memory chips, an error correcting code approach is found to be suitable. Various codes are considered and a lookup table approach is proposed for encoding and decoding. We are then able to give estimations for the redundancy level to be provided on nanochips, so as to make their mean time between failures acceptable. It is found that, for logic chips, space redundancies up to a few tens are required, if mean times between failures have to be of the order of a few years. Space redundancy can also be traded for time redundancy. As for memory chips, mean times between failures of the order of a few years are found to imply both space and time redundancies of the order of ten

Cellular Automata

Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented